Aircraft: C172
Phase of flight: Landing
Anomaly: Deviation / Discrepancy - Procedural Other / Unknown; Inflight Event / Encounter Fuel Issue

The trip was my first long distance; multiple fuel stop cross country plan in unfamiliar territory as PIC. When I called Flight Service for a briefing I was not notified that one of the airports where I intended to land for fuel was closed for maintenance. I fully fueled the airplane and departed our home airport. The takeoff was a soft/short field type due to the length of our runway; the length of the grass on the runway and my load of two passengers and one duffel bag. I made the ascent to cruising altitude of 3;500 MSL. When I reached cruising altitude I leaned the mixture according the POH. During the first leg of the flight I was cruising at 3;500 MSL and getting a little push from a tailwind. I was monitoring my ground speed and it was consistent throughout this portion of flight. The first fuel stop was exactly 2 hours into the trip and both fuel gauges indicated that my tanks were more than half full. The next stop was planned to be 90 minutes according to my navigational equipment so I thought I had enough fuel to make the airport with reserve fuel so I continued without the first fuel stop. I was very conscious of my fuel situation as I continued to monitor the fuel gauges. I was also monitoring my ground speed. By the time I had flown well beyond the last available alternative fuel stop before my planned stop; my fuel gauges read one quarter full but were heading toward empty at a faster rate than the first three quarters of the burn. I also noted that I had lost about 10 mph of ground speed for about 10 minutes during this last portion of flight so I considered turning around and going back. I quickly realized that I was midway between the alternative and destination; so turning around into a headwind was not a viable option. I was getting uncomfortably low on fuel when I announced my approach at 10 miles and the FBO informed me that the airport was closed. I was beginning to plan my descent from 3;500 MSL to pattern altitude. Instead I pulled the throttle back to 1;500 RPM and trimmed the nose up to slow the plane; conserve fuel and buy time. While the airplane gained 500 feet in altitude I made a standard rate turn to the left trying to identify an alternative landing area. I noticed that my fuel gauges were both bouncing off of empty so I knew I had some fuel; but not much. There were three restricted airports within gliding distance but I was unsure of their condition. I asked the FBO whether it was possible to land and was informed that I needed to declare an emergency to do so. I believed that was my best option to land safely. I was five miles from the airport at 4;000 MSL and had slowed to best glide speed. I deployed 30 degrees of flaps and slipped the airplane to lose altitude in a steep descent. The angle of my approach was extreme so just prior to the flare I throttled up and made a safe and smooth landing. Because the airport was closed I could not depart so we rented a car and continued our journey on wheels. C172 pilot reports over flying his first fuel stop on a cross country flight due to more than half of the initial fuel remaining and more than half the flight completed. Upon arrival at destination with minimal fuel the airport is found to be closed for construction. An emergency is declared to land on the closed runway.